Can anyone suggest a reference source which discusses the physics of
steering a motorcycle, a technique known to bikers as "counter-steering"?
I have now seen two articles on the subject in two motorcycle magazines
(Motorcycle Consumer News years ago and Motorcycle Roads, Dec. 96)) in
which the physics of counter-steering is bad, misleading, and wrong. The
authors give neither their qualifications for writing such an article nor
any reference sources. Before I respond in a letter, I would like to back
up my comments with a good reference source(s).
For those unfamiliar with counter-steering, the process is known as: Push
right, lean right, go right; Push left, lean left, go left. "Push right"
means pushing forward on the right handgrip in order to lean right into a
curve going off to the right. The amount of lean needed is a function of
bike speed and the radius of the curve (Tan (theta) = v^2/Rg ). Racers
also shift body weight signficantly but touring bike riders do not.
Here is my understanding of how it works:
A motorcycle going straight on a horizontal surface has an angular momemtum
pointing horizontally to the left due to the rotation of the wheels.
Pushing forward on the right handgrip creates an unbalanced upward torque:
Vector R (right) cross Vector F (forward) = Vector Tau (up) = Vector dL/dt
(up).
The initially upward torque creates an initially upward Delta L which, when
added to the initial angular momemtum will give a final angular momentum
which is pointing up and to the left meaning that the bike is leaning to
the right. Leaning to the right and not sliding on the surface (as it
might on ice) means that there is a frictional force to the right which is,
of course, the centripetal force needed to change the direction of the
motorcycle. [My students know how to finish this sentence: "Vector math was
invented because...." "...IT WORKS !!!" they will shout]. While leaning
towards the right, there is a slight "coning effect" of the tires. The
coning effect is why a styrofoam coffee cup will roll in a circle: All
points on the cup will have the same angular velocity meaning that the
larger the radius of the cup, the greater the tangential velocity ( v = wr
).
The above phenomenon can be demonstrated with the standard bicycle wheel
found in physics lecture/lab room.
If you have anything to add or corrections to make to my understanding of
"counter-steering" a motorcycle, I would greatly appreciate your response.
NO ILLUSIONS -=> Should I respond (in a letter) to the articles mentioned
above, I have no illusions that more than just a few readers would
understand what I was talking (or torquing) about. My order of magnitude
estimation of the fraction of readers who would understand the correct
physics of "counter-steering" is 10^-3.
For your amusement (or it "for your sadness and horror"), here is some of
the "bad physics" described in the article: Inertia is a force as in (1)
"Now let us see how we can harness the forces of gravity and inertia to
steer our motorcycles precisely in the direction we want to go" and (2)
"...we steer by shifting the contact patch to balance inertia." whatever
that means. Twice he states that "Centrifugal force balances gravity"
(otherwise, he implies, the bike would fall over). On a digram,
centrifugal force is drawn as an arrow pointing outward from the center of
the bike and gravity is drawn as an arrow pointing downward from the center
of the bike. He explains counter-steering this way: Pushing forward on the
right handgrip turns the wheel to the left causing the contact patch to
move from directly underneath the tire to the right side of the tire where
the coning effect and traction provide 90% of the leaning and turning force
while gyroscopic precession provides the other 10% (stated with no
reference to research or data). "Gyroscopic precession does apply a force
which tries to lean the top of a spinning gyro towards the right when the
axle is turned to the left, which is exactly what happens to the front
wheel of a motorcycle when we countersteer." "It can contribute only about
10% of the leaning force. Out-tracking of the contact patch provides the
other 90%. Traction is just much stronger than precession."
QUESTION: Should I even bother to respond to the article since the "common
sense" (which isn't common) of the vast majority of the readers will agree
that outward centrifugal force balances gravity and they will never have
heard of angular momentum?
ONE INTERESTING ASIDE: At a Chicago Section AAPT meeting, I asked the
participants (more college profs than high school teachers) to pick up a
ruler or pencil to represent the handlebars of a motorcycle and hold the
ends with both hands to represent riding a motorcycle straight ahead. Then
I asked them to exaggerate the turning of the handlebars when going around
a right hand curve. The vast majority, without thinking, car-steered the
handlebars the wrong way. After using a bicycle wheel to demonstrate
counter-steering followed by showing what tends to happens to a single
engine airplane when it makes a right or left hand turn, Dr. T. H. Jeong
(of holography fame) from Lake Forest College got up and showed what tends
to happen to hovering helicopter when someone exerts an torque by climbing
aboard on one side. Such interesting exchange of ideas. Such PHUN !!
A SECOND INTERESTING ASIDE: If you do not ride a motorcyle, you can
demonstrate counter-steering to yourself while riding a bicycle. While
riding at a safe, reasonable speed, gently push forward on one of the
handgrips and notice what happens to the bicycle. On a bicycle, body
weight is greater than bicycle weight and I'm sure that shifting body
weight slightly (and perhaps sub-conscientiously) contributes more to the
lean than pushing (or pulling) on the handgrips.
A THIRD INTERESTING ASIDE: The author of the Motorcycle Roads article
implies that riders who do not conscientiously counter-steer their bike
must steer in a different way: "If you haven't been balancing and steering
by pushing on the grips, you'll be amazed at how much better you can
control your machine by counter-steering." For three years, I was a
certified instructor for the Motorcycle Safety Foundation and during that
time I taught their Riding and Street Skills course. Often, an experienced
rider would take the course who had never never heard of counter-steering
(push right, go right; push left, go left) and they wondered how they had
been steering their bikes before they had taken the course. After many
such discussions and analysis, I discovered that they had subconsciously
learned to gently push forward on one handgrip while pulling gently on the
other handgrips. They had learned this subconsciously because of the
immediate feedback of trying to car-steer the bike made it go the wrong way
and they were able to make the bike go the correct way by subtle and
unconscious changes in force on the handgrips. What happens to a biker who
does not consciously counter-steer his bike when an emergency happens and
he panics? Quoting from Rider magazine (March 1989), "...accident
investigators routinely uncover evidence of panic-stricken riders pushing
on the wrong side in an attempt to car-steer the wheel away from the
approaching hazard."
Now for your own proof: Remember when you were a kid riding your bike on
the sidewalk because you weren't old enough to ride in the street?
Remember when you got too close to the edge of the sidewalk and you tried
to suddenly car-steer the bike back to the center of the sidewalk? Do you
remember what happened? For some explained reason, the bike leaned the
wrong way and you rode off into the grass, perhaps even falling over. Do
you remember what you said to yourself? "That's strange. When I grow up,
I'm going to take physis in order to learn what happened here."
AND YOU DID !! That's why you're still reading this. My order of magnitude
estimate of the fraction of Phys-listers who skimmed this far is 10^-1 and
of those who actually read this far is 10^-2. That's ok. I do the same.
We all do. I still learn a lot from my known and unknown physics phriends.
Sorry I got carried away. It must be winter break time. All I really want
is a good reference on the physics of motorcycling. Please respond if you
know of one.
Thank you, and again, Happy New Year.
David (a.k.a DiRT)
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David R. Thiessen FUN + PHYSICS = PHUN
Science Department PHYSICS IS PHUN !!
Deerfield High School
1959 North Waukegan Road Education increases your freedom
Deerfield, IL 60015 Because It Increases Your Options !!
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School phone (708) 405-8488 Education will enrich your life
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Apples instead of driving them bananas ??
dthiessn@nslsilus.org (Quote sources long forgotten)
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